I have the same problem - I thought about it once and I think it is because those colours are the least used in the common E6 series of values - blue and grey are only used in 68, and white not at all. And really in a lot of cases you only see "E3" values - 10,22,47. I'd do an analysis of the frequency of use of the colours in E12 but I have to get to work :-(

There's a nice graphic here showing all the E series and how they overlap:

@ Crusty: A good point about the failure of solder joints from thermal stress. I've repaired several older Amatuer Radio tranceivers. In almost all cases, the repair was to re-solder a power component in either the power amp or power supply.

The other failure that I've seen frequently is a solder joint failing due to repeated mechanical stress. Power jacks seem to be especially suseptible to this....

Another skill is reading resistor color code without needing to look it up on wikipedia, but sometimes it can be misleading. Some manufacturers are not overly caring about the quality of the paints they use, often it can be difficult to distinguish between brown, red, and orange even when the resistor body color is light such as beige.

I recently ordered some 4K99 1% resistors made by KOA Speer, when they arrived I had to put one on the ohmeter to verify the value - its colors were green white white brown brown which indicates 5K99 1%. Then I realized that the first band was actually yellow but transparent to the blue body color, which converted it visually to green. An almost gotcha.

Crusty - Since I rarely throw things away, I've been having a bit of a field day fixing up broken items I've had buried in my garage. I can't help you with the case though. Mechanical things are not my forte.

I have come across a number of power packs where the main resistor was not provided with a sufficient heat sinked, or the copper traces were too small for the thermal energy disipated. You end up with a dry joint in the end, but from thermal stress.

One more reason for soldering and repair skills, is in a companies returns department. To get the best quality control a returns department needs to actually tear down the faulty items and feed problems found back into the production cycle. On a number of third part quality audits I have undertaken, the returns process and how it feeds into the production cycle has often been the biggest audit failure.